Conservation of Energy
Imagine that you have an empty jar. Now, imagine filling it up with jellybeans and then tightly sealing it so that the jar remains shut no matter what. You can shake the jar, roll it around, toss it up in the air, run around in a circle with it, etc., but since the jar is sealed tightly shut the jellybeans will remain safe and secure inside the jar. No jellybeans will escape and no more jellybeans will be added inside the jar. So, the amount of jellybeans you originally put inside the jar is the amount of jellybeans you end up with. Essentially, you don't lose any jellybeans and you don't gain any jellybeans--the amount of jellybeans remains the same. Similarly, this concept exists in physics as the conservation of energy. '''The Conservation of Energy Law' states that energy is neither created nor destroyed. In an ideal closed system, where no external factors (i.e...friction) act, the total mechanical energy remains constant. There are two important things to remember: 1. To reiterate, the energy of a closed system remains the same in the beginning and in the end. Initial Potential Energy + Initial Kinetic Energy = Final Potential Energy + Final Kinetic Energy, or more simply stated PEi + KEi = PEf + KEf. 2. The total energy of a system is the sum of its potential energy and its kinetic energy. Total Energy = Potential Energy + Kinetic Energy or Et = PE + KE. TABLE OF CONTENTS 1. Historical Development of The Conservation of Energy Law 2. Types of Energy a. Potential Energy b. Kinetic Energy c. Mechanical Energy 3. Thermodynamics 4. Check your understanding! TYPES OF ENERGY Energy can exist as potential energy or as kinetic energy. It may be converted from potential energy to kinetic energy or vice versa but it is neither created nor destroyed. a. Potential Energy The gravitational potential energy of an object is the work done by a constant gravitational force F = mg on the object to move it from a certain position to another position. More on Potential Energy b. Kinetic Energy An object's kinetic energy is the energy that a body possesses due to its motion. More on Kinetic Energy c. Mechanical Energy Mechanical Energy is the energy that an object has due to its stored energy (potential energy) or due to its motion (potential energy). Objects possessing mechanical energy can do work. More on Mechanical Energy The Law of Conservation of Energy states that an object's mechanical energy remains constant in a closed system. THERMODYNAMICS Thermodynamics is a branch of physics that investigates the movement of energy and how energy causes movement. It deals with the energy and work of a large system. Essential to thermodynamics is the Conservation of Energy principle. The first law of thermodynamics states h = h + u^2/2 and this formula was derived using the Law of Conservation of Energy. h = enthalpy = e + pv p = pressure v = volume u = velocity (Note: Enthalpy is the sum of the internal energy of matter and the product of its volume and pressure.) For more information on the derivation of the first law of thermodynamics, feel free to visit http://www.grc.nasa.gov/WWW/K-12/airplane/thermo1f.html Thermodynamics CHECK YOUR UNDERSTANDING Here are some review questions relating to the Conservation of Energy for you to check your understanding: a. Consider the falling motion of the ball in the following two frictionless situations. For each situation, indicate what type of forces are doing work upon the ball. Indicate whether the energy of the ball is conserved and explain why. Finally, indicate the kinetic energy and the velocity of the 2-kg ball just prior to striking the ground. For questions b and c, refer to the image below: Conservation_of_energy.gif b. As the object moves from point A to point D across the frictionless surface, what happens to the sum of its gravitational potential and kinetic energies? c. When will the object have minimal potential energy? Answers: a. Gravity is the only force that is doing work. It is acting on the system internally, so the total mechanical energy remains conserved. Therefore, all 100J of Potential Energy is converted to Kinetic Energy when the ball hits the ground, at the bottom of the hill. Using the equation KE = mv^2 , we can determine that the velocity is 10 m/s^2. b. The sum of the object's potential and kinetic energies (it's mechanical energy) remains the same throughout its path of travel whenever no external forces (such as friction) are acting on it. c. At Point B, the object will have minimal potential energy. Potential energy depends on height so when the height is lowest, the potential energy is lowest as well. When the potential energy is low, the kinetic energy is high.